Talk:Chirality (physics)

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Help with this template Comments: edit – history – watch – refresh Chirality is explained wrong in this article. Chirality is a Lorentz invariant quantity. The spin projection is Helicity. For massless particles these are the same. But the point is that, for massive particles, helicity depends on the frame of reference, but chirality does not. Unfortunately, chirality is a very abstract concept, and I haven't got an intuitive explanation for it. To re-iterate: it is not the spin projection on the direction of motion, but co-incides with this (only) for the case of massless particles.

Alterations and restructuring are needed to properly represent use and meaning of the word chirality. Please join the multi-disciplinary discussion on Talk:Chirality. --Cigno 22:12, 15 November 2005 (UTC)

Contents 1 Merge with Helicity 2 Don't merge with helicity 3 Chirality Explained Wrong 4 Chirality Fixed Up a Bit 5 Absolute and Relative Chirality 6 Summary Chart of Chirality vs Helicity

[edit] Merge with Helicity

Two reasons.

• For massless particles, there's no difference between chirality and helicity, except for numerical factor.
• For massive particles, the two are often confused. Even this article talks about "relative chirality, which depends on the observer’s reference frame", but what it really means is that massive particles have relative helicities. As the article correctly says in the section 2, chirality is given by the operator γ⁵. Chirality is Lorentz-invariant, and helicity is not. --Itinerant1 05:27, 4 September 2006 (UTC)

If you're an expert on the subject (or have knowledge) by all means please merge. Radagast83 19:58, 28 October 2006 (UTC)

[edit] Don't merge with helicity

• The two quantities are often conflated and, unless expertly done, merging the articles is only likely to encourage this misconception to persist. It may even be worth adding "not to be confused with helicity" or such into the first paragraph of this article, but I don't feel I'm expert enough to draw the appropriate distinction yet.

[edit] Chirality Explained Wrong

Chirality is explained wrong. It is not the projection of the spin in the direction of motion. Helicity is in fact the spin projection on the direction of motion (and therefore depends on the reference frame). Chirality is a much more abstract concept, and it does not depend on the frame of reference. For massless particles (and only for those), chirality and helicity are the same. For massive particles they are different - one independent of the frame of reference, the other not. So, for massless particles, a chirality left-handed particle is always helicity left-handed. But for massive particle, a chirality left-handed particle can be helicity right-handed. See for example pion decay, where this effect (and its dependence on the mass of the particle) plays a major role. It is however true, that parity transforms chirality left-handed particles to chirality right-handed ones, as well has helicity left-handed ones to helicity right-handed ones (and vice versa).

[edit] Chirality Fixed Up a Bit

The old definition is now (correctly) called helicity. In the new definition, chirality tells us whether a particle transforms in a right or left handed representation of the poincare group. Someone else can feel free to incorporate more detail. Drkarat (talk) 18:20, 3 June 2008 (UTC)

[edit] Absolute and Relative Chirality

I think the material discussing "absolute" vs. "relative" chirality is misleading and should be removed. Chirality is chirality; the terms "absolute chirality" and "relative chirality" are certainly not in common usage and seem to have been invented in this article. If there are no objections, I'll try to clean this up (and also make the definitions of chirality and helicity clearer) when I get the time. Aiwendil42 02:15, 11 July 2007 (UTC)

I agree entirely. Rather than this absolute v. relative discussion, a section on chirality vs helicity would clarify things. I've tried to clean out what I believe to be inaccuracies, though it was in a section about what things "are called" which is always debatable.PhysPhD 23:38, 4 August 2007 (UTC)

Though the recent changes were a step in the right direction, I think the above Chirality Explained Wrong criticism has not been adequately addressed. We need a clear definition of chirality that differs from helicity. Frankly, I don't know how chirality is defined geometrically, only that the Chirality operator is represented on fermions as γ⁵. Also, how does the Pauli-Lubanski pseudo-vector fit into this?PhysPhD 21:27, 30 August 2007 (UTC)

Chirality is definitely defined wrong in this article. One way to define it is through Lorentz transformation: left and right spinors transform differently under the Lorentz group —Preceding unsigned comment added by 128.141.132.197 (talk) 14:23, 5 November 2007 (UTC)

[edit] Summary Chart of Chirality vs Helicity

Chirality is explained incorrectly, as noted above. The explanation starts by showing helicity but calling it chirality. Helicity is a physical space kind of thing. If the fingers of your right hand curl in the direction of spin, and the thumb of the same hand points in the direction of the velocity (momentum direction), you have right hand helicity. If it works in the same way for your left hand, you have left hand helicity.

In contrast, chirality is related to the charge of the weak force field the particle feels. It is not related to the physical space, per se, but rather to an abstract space (the Dirac spinor space and the associated γ⁵ matrix found therein.) For example, a chiral left hand election has a weak charge of -1/2, a chiral left hand neutrino +1/2, and any chiral right hand particle, zero. These have little to do helicity, EXCEPT a funny thing happens as particle speed approaches that of light. If one follows the math, one sees that helicity then approaches chirality, in effect. For massless particles, as noted above, the speed is that of light, so helicity and chirality are the same.

The use of the terms "left hand chirality" and "right hand chirality" probably has its origin in that phenomenon (i.e., what happens as v --> c), but chirality really doesn't have a kind of physical handedness like helicity. The choice of nomenclature, early on, has led to immense confusion over the years.

To see an explanation and summary of the differences and similarities between chirality and helicity (those covered here and more) in chart form, go to www.quantumfieldtheory.info and click on the appropriate link near the bottom of the page. —Preceding unsigned comment added by Bob108 (talk • contribs) 21:25, 22 October 2007 (UTC) Bob108 21:29, 22 October 2007 (UTC)